Today you are free to explore Ishigaki.
If diving is your thing, there are several bilingual tour operators on the island that will be able to help you out, and shops to rent gear. Prices are pretty similar amongst the operators, so its hard to go wrong. Trips out on boats, kayaks or to go snorkelling are also readily available.
If you're not wanting to get out in the water or it's just not the season for it, you can still admire the views. There are walking trails through the palm forests and viewing platforms in Cape Tamatori where you can check out the scenery.
After a long day of walking or snorkelling (or let's face it, a long day of kicking back and enjoying yourself), Ishigaki has a lot to offer in the way of cuisine, particularly Ishigaki beef or soba. If you fancy a drink, the Okinawans are very good at this too, so feel free to wander around and find a local bar.